Such a break divisor is automatically of degree \(g\) , since \(g=b_1(G)+\sum _{v\in V(G)}h(v)\) . By [1]}, an admissible divisor is \(\phi _G^{can}\) -stable if and only it is a break divisor. So Theorem REF  (and thus [2]}) also recovers the main result of [3]} stating that every divisor of degree \(g\)  on a metric graph \(\Gamma \)  has a unique break divisor representative. In Figure REF  we show the induced polyhedral decomposition of \(\operatorname{Pic}_g(\Gamma )\)  in the fiber over a stable tropical curve of genus whose underlying graph is a theta-graph (without vertex weights).
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